The sharpness of convergence results for $q$-Bernstein polynomials in the case $q>1$

Sofiya Ostrovska

Displaying similar documents to “The sharpness of convergence results for $q$ -Bernstein polynomials in the case $q > 1$ ”

Approximation properties of bivariate complex $q$ -Bernstein polynomials in the case $q > 1$

Nazim I. Mahmudov (2012)

Czechoslovak Mathematical Journal

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In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate $q$ -Bernstein polynomials for a function analytic in the polydisc $D_{R_{1}} \times D_{R_{2}} = {z \in C : | z | < R_{1}} \times {z \in C : | z | < R_{1}}$ for arbitrary fixed $q > 1$ . We give quantitative Voronovskaja type estimates for the bivariate $q$ -Bernstein polynomials for $q > 1$ . In the univariate case the similar results were obtained by S. Ostrovska: $q$ -Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein...

On the Degre of L1-aproximation by Modified Bernstein Polynomials

Suresh Prasad Singh, O.P. Varshney, Govind Prasad (1983)

Publications de l'Institut Mathématique

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A note on the modified $q$ -Bernstein polynomials.

Kim, Taekyun, Jang, Lee-Chae, Yi, Heungsu (2010)

Discrete Dynamics in Nature and Society

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Convexity and variation diminishing property for Bernstein polynomials in higher dimensions

Marek Beśka (1989)

Banach Center Publications

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$q$ -Bernstein polynomials associated with $q$ -Stirling numbers and Carlitz's $q$ -Bernoulli numbers.

Kim, T., Choi, J., Kim, Y.H. (2010)

Abstract and Applied Analysis

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On the approximation of analytic functions by the $q$ -Bernstein polynomials in the case $q > 1$ .

Ostrovska, Sofiya (2010)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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A pointwise approximation theorem for linear combinations of Bernstein polynomials.

Guo, Shunsheng, Yue, Shujie, Li, Cuixiang, Yang, Ge, Sun, Yiguo (1996)

Abstract and Applied Analysis

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A new generating function of ( $q$ -) Bernstein-type polynomials and their interpolation function.

Simsek, Yilmaz, Açıkgöz, Mehmet (2010)

Abstract and Applied Analysis

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The Lower Estimate for Bernstein Operator

Gal, Sorin G., Tachev, Gancho T. (2013)

Mathematica Balkanica New Series

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MSC 2010: 41A10, 41A15, 41A25, 41A36 For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.

Displaying similar documents to “The sharpness of convergence results for q -Bernstein polynomials in the case q > 1 ”

Displaying similar documents to “The sharpness of convergence results for $q$ -Bernstein polynomials in the case $q > 1$ ”